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On Koenigs' ratios for iterates of real functions

Published online by Cambridge University Press:  09 April 2009

E. Seneta
E. Seneta
Affiliation:
Australian National University Canberra, ACT
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In a recent note, M. Kuczama [5] has obtained a general result concerning real solutions φ(x) on the interval 0 ≦ x < a ≦∞ of the Schröder functional equation providing the known real function satisfies the following (quite weak) conditions: f(x) is continuous and strictly increasing in ([0 a);(0) = 0 and 0 <f(x) <x for x ∈ (0, a); limx→0+ {f(x)/x} = s; and f(x)/x is monotonic in (0, a).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 10 , Issue 1-2 , August 1969 , pp. 207 - 213
Copyright
Copyright © Australian Mathematical Society 1969

References

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